Question

Calculate. $$\frac{d}{d x}\left(\int_{}^{A} \sin t^{2} d t\right)$$

   Calculate.
$$\frac{d}{d x}\left(\int_{}^{A} \sin t^{2} d t\right)$$

Calculus: One and Several Variables

Calculus: One and Several Variables

Saturnino L. Salas,… 10th Edition

Chapter 5, Problem 22

Instant Answer

Solved by Expert Harmender Singh Yadav

10/30/2021

Step 1

Step 1: We are given the expression $\frac{d}{d x}\left(\int_{}^{A} \sin t^{2} d t\right)$ and we are asked to find its derivative. Show more…

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Calculate. $$\frac{d}{d x}\left(\int_{}^{A} \sin t^{2} d t\right)$$

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Key Concepts

Differentiation of Constant Functions

When differentiating a function that does not depend on the variable, the derivative is zero. In this problem, since the integral from a constant value to A (a constant) results in a constant, its derivative with respect to x is 0.

Fundamental Theorem of Calculus

This theorem links differentiation and integration, stating that if an integral has variable limits, its derivative involves evaluating the integrand at those limits. However, when both limits are constants, as in this case, the differentiated integral represents a constant, leading to a derivative of 0.

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